Question

QUIZZZ

HP dari persamaan
2x + 5y = 23
3x - 2y = 2

adalah

#itu Bukan akun Gw
​

Answer 1

[tex] \begin{cases} \sf 2x + 5y = 23 \dots(1) \\ \sf 3x - 2y = 2 \ \ \dots(2) \end{cases}[/tex]

 

Eliminasi (1) dan (2)

[tex] \begin{aligned} \sf 2x + 5y = 23 \ | \sf\times 3| \ \diagup\!\!\!\!\!6x + 15y &= \sf 69 \\ \sf 3x - 2y= 2 \ \ \ | \sf\times 2| \ \underline{\qquad \qquad \quad \ \ \ }\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\diagup\!\!\!\!\! \sf 6x \ - \ 4y &= \sf 4 \ - \\ \sf 19y &= \sf 65 \\ \sf y &= \sf \frac{65}{19} \end{aligned}[/tex]

 

Substitusi y ke (1)

[tex] \begin{aligned} \sf 2x + 5y &= \sf 23 \\ \sf 2x + 5\left(\frac{65}{19}\right) &= \sf 23 \\ \sf 2x + \frac{325}{19} &= \sf 23 \\ \sf 2x &= \sf \frac{437 - 325}{19} \\ \sf 2x &= \sf \frac{112}{19} \\ \sf x &= \sf \frac{ \ \diagup\!\!\!\!\!\!\!112}{19} \times \frac{1}{\not\!2} \\ \sf x &= \sf \frac{56}{19} \end{aligned}[/tex]

 

HP = {⁵⁶/₁₉, ⁶⁵/₁₉}

⌗SDaze ⋆࿐໋₊

Answer 2

Verified answer

Jawab:

[tex]\displaystyle \textrm{HP}=\left \{ \frac{56}{19},\frac{65}{19} \right \}[/tex]

Penjelasan dengan langkah-langkah:

[tex]\displaystyle\left\{\begin{matrix}2x+5y=23\\ 3x-2y=2\end{matrix}\right.[/tex]

Jika diubah ke bentuk matriks menjadi

[tex]\displaystyle \begin{pmatrix}2 & 5\\ 3 & -2\end{pmatrix}\binom{x}{y}=\binom{23}{2}[/tex]

Berdasarkan persamaan matriks [tex]\displaystyle AX=B[/tex]

[tex]\begin{aligned}AX&\:=B\\AA^{-1}X\:&=A^{-1}B\\IX\:&=A^{-1}B\\X\:&=A^{-1}B\end{aligned}[/tex]

Metode invers matriks

[tex]\begin{aligned}\binom{x}{y}&\:=\begin{pmatrix}2 & 5\\ 3 & -2\end{pmatrix}^{-1}\binom{23}{2}\\\binom{x}{y}\:&=\frac{1}{2(-2)-5(3)}\begin{pmatrix}-2 & -5\\ -5 & 2\end{pmatrix}\binom{23}{2}\\\binom{x}{y}\:&=-\frac{1}{19}\binom{-2(23)-5(2)}{-5(23)+2(2)}\\\binom{x}{y}\:&=-\frac{1}{19}\binom{-56}{-65}\\\binom{x}{y}\:&=\binom{\frac{56}{19}}{\frac{65}{19}}\end{aligned}[/tex]